Multicommodity network flow models with FIFO transshipment handling policies

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2011-08

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Abstract

Integer multicommodity network flow (MCNF) models have applications in various areas like logistics, freight transportation, telecommunication and manufacturing. In this thesis we study an extension of the integer MCNF problem (MCNF-FIFO) where commodities are handled (processed) in a first-in-first-out (FIFO) order at each transshipment location and resource capacities are shared across arcs in the network. The objective of the MCNF-FIFO model is to find feasible routes for all commodities from their origins to destinations while minimizing the total transportation and holding cost or the sum of delivery times. We formulate the MCNF-FIFO problem on a time-space network and develop three different integer-programming (IP) formulations for the FIFO constraints, and two IP formulations for the flow conservations requirements. Since these formulations have a very large number of variables and constraints, we develop various algorithmic strategies to obtain good quality solutions quickly. The first strategy is to reduce the problem size by using properties of the optimal solution. We develop novel problem reduction and decomposition techniques that eliminate variables and constraints, and decompose the problem into smaller components. To further reduce the problem size, we classify the FIFO constraints into different categories by utilizing the relationships between different commodities, and provide specialized formulations for each of these categories so as to reduce the number of FIFO constraints significantly. The second strategy is to develop heuristic algorithms that provide near-optimal solutions to the MCNF-FIFO problem. Our first algorithm is an optimization-based heuristic that solves a relaxed MCNF-FIFO model with a limited number of FIFO constraints. Then, it removes the remaining infeasibilities in the solution of the relaxed MCNF-FIFO model using a repair heuristic to obtain a feasible solution. We develop two other heuristic algorithms that are stand-alone construction heuristics that build a feasible solution from scratch. To assess the effectiveness of the modeling and algorithmic enhancements, we implement the methods and apply them to three real life test instances. Our tests show that the problem reduction techniques are very effective in reducing the solution times. Among the heuristic algorithms, the optimization-based heuristic performs the best to find near-optimal solutions quickly.

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